A proposal for a numerical method based on the complete solution collocation method is presented to solve the cable-stayed bridge engineering structural problem. This complete function collocation method is presented from the viewpoint of calculating the pretension forces required for the final completed bridge structure, which is one of the most important and practical considerations in cable-stayed bridge design. The complete function collocation method is used to calculate stay cable forces by solving a set of partial differential equations. The study shows that this mesh-free collocation method can be used to solve practical structural engineering problems and provides an alternative to traditional finite element methods. A simple two-dimensional cable-stayed bridge is presented and is solved to illustrate this numerical method. Governing equations of deformation for a bridge structure are formulated in either Eulerian or Lagrangian coordinate systems according to the situation. Point loads due to stay cables on bridge pylons and bridge deck are modelled by Fourier or Gaussian representations. Transverse natural frequencies of stay cables subject to no body forces and caused by flow-induced vibration due to blowing wind are proposed. The preliminary computational procedure presented in this paper provides the basis for further analysis toward more realistic cable-stayed bridges, which would include nonlinear effects, live loadings and construction stage loadings.